(x+3)(x+6) Which of the following is equivalent to the given expression? Choose 1 answer: (A) 2x^(2)+9x+18 (B) x^(2)+9x+9 (C) 2x^(2)-3x+18 (D) x^(2)+9x+18

Apply distributive property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the first terms, the outer terms, the inner terms, and the last terms together. (x+3)(x+6) = x*x + x*6 + 3*x + 3*6Perform multiplication: Perform the multiplication for each term. x*x = x^2 x*6 = 6x 3*x = 3x 3*6 = 18Combine like terms: Combine like terms (6x and 3x). x^2 + 6x + 3x + 18 = x^2 + (6x + 3x) + 18 = x^2 + 9x + 18Match resulting expression: Match the resulting expression with the given choices. The expression x^2 + 9x + 18 matches choice (D).

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(x+3)(x+6)
Which of the following is equivalent to the given expression?
Choose 1 answer:
(A)
2x^(2)+9x+18
(B)
x^(2)+9x+9
(C)
2x^(2)-3x+18
(D)
x^(2)+9x+18

$(x+3)(x+6)$ $\newline$ Which of the following is equivalent to the given expression? $\newline$ Choose $1$ answer: $\newline$ (A) $2 x^{2}+9 x+18$ $\newline$ (B) $x^{2}+9 x+9$ $\newline$ (C) $2 x^{2}-3 x+18$ $\newline$ (D) $x^{2}+9 x+18$

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Math Problems

Algebra 1

Identify equivalent linear expressions

Full solution

(x+3)(x+6)

\newline

Which of the following is equivalent to the given expression?

\newline

Choose

1

answer:

\newline

(A)

2 x^{2}+9 x+18

\newline

(B)

x^{2}+9 x+9

\newline

(C)

2 x^{2}-3 x+18

\newline

(D)

x^{2}+9 x+18

Apply distributive property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the first terms, the outer terms, the inner terms, and the last terms together. $\newline$ $(x+3)(x+6) = x \times x + x \times 6 + 3 \times x + 3 \times 6$
Perform multiplication: Perform the multiplication for each term. $\newline$ $x \times x = x^2$ $\newline$ $x \times 6 = 6x$ $\newline$ $3 \times x = 3x$ $\newline$ $3 \times 6 = 18$
Combine like terms: Combine like terms $6x$ and \(3x\＂). $x^2 + 6x + 3x + 18 = x^2 + (6x + 3x) + 18 = x^2 + 9x + 18$
Match resulting expression: Match the resulting expression with the given choices. $\newline$ The expression $x^2 + 9x + 18$ matches choice (D).